Sticky-threshold diffusions, local time approximation and parameter estimation

Alexis Anagnostakis, Sara Mazzonetto

Published 2024-03-13Version 1

We study a class of high frequency path functionals of a diffusion with a sticky-oscillating-skew (SOS) threshold, including the case of a sticky-reflection, and establish convergence to the local time. This extends existing results on sticky, oscillating (regime-switching) and skew or reflecting diffusions in several directions. First, it considers any normalizing sequence $(u_n)_n $ that diverges slower than $n$. Second, it allows combinations of these features. Based on this, and an approximation of the occupation time, we devise consistent skew and stickiness parameter estimators.